2007 H2 Mathematics Paper 2 Question 9

Permutations and Combinations (P&C)

Answers

(ia)
479,001,600{479,001,600}
(ib)
46,080{46,080}
(iia)
39,916,800{39,916,800}
(iib)
86,400{86,400}
(iic)
240{240}

Full solutions

(ia)
Number of different possible orders
=12!=479,001,600  ■\begin{align*} &= 12! \\ &= 479,001,600 \; \blacksquare \end{align*}
(ib)
Number of different possible orders
=6!×(2!)6=46,080  ■\begin{align*} &= 6! \times (2!)^6 \\ &= 46,080 \; \blacksquare \end{align*}
(iia)
Number of different possible arrangements
=11!=39,916,800  ■\begin{align*} &= 11! \\ &= 39,916,800 \; \blacksquare \end{align*}
(iib)
Number of different possible arrangements
=5!×6!=86,400  ■\begin{align*} &= 5! \times 6! \\ &= 86,400 \; \blacksquare \end{align*}
(iic)
Number of different possible arrangements
=5!×2!=240  ■\begin{align*} &= 5! \times 2! \\ &= 240 \; \blacksquare \end{align*}